The program uses regular rectangular areas. Then 3 or more sections are picked
out of the area and the latitude and longitude of the center of the section is
entered in a regression program and coefficients are generated. Using these
coefficients the latitude and longitude of every section in the area can be
predicted If every section is exactly square, the same size, and the lines are
exactly north/south and east/west the program predicts an extremely accurate
latitude/longitude. However this is seldom the case. Township lines are
normally adjusted every 4th or 5th township to take care of the curvature of
the earth. If this were the only irregularity the program would still predict a
very accurate latitude/longitude of each section by choosing rectangular areas
delimited by these adjustments. Its seems that for no apparent reason townships
are often offset a considerable amount, sections are elongated or shrunk, 1/2
townships and 1/2 ranges are added. In Oregon even 3/4 townships are used. In
Arkansas the lines are skewed over 1 degree. This of course requires the areas
to be broken down into smaller areas, and even then the accuracy is impaired.
1:100000 scale BLM or USGS maps are used.
Take a look at this BLM map. Notice the area
labeled H25A. There are also some 1/2 township or range areas.
Now take a closer look at the area.
Three sections were used to calculate the coefficients. The sections, latitude, longitude, coefficients and R squared is shown in the printout.
h25a 10-27-2001 09:49:03
Long AX= 438564.78 BX= -64.017538 R^2= 0.99998521177
Lat AY= 136354.47 BY= -52.173293 R^2= 0.99999880769
- - A C T U A L - - - - C A L C U L A T E D -
T/R/S LAT / LONG LAT / LONG T/R/S
13S 42E 8 36 49.102 117 25.886 36 49.097 117 25.874 13S 42E 8
16S 43E23 36 31.712 117 16.281 36 31.706 117 16.272 16S 43E23
15S 42E 1 36 39.521 117 21.585 36 39.532 117 21.606 15S 42E 1
For 17 states totaling 1,598,615 square miles, 1980 factors were used. This breaks down into 807 sections or about 22.5 townships per factor.
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